No, you cannot use the conditional to convey the habitual-past aspect. That is expressed using the imperfect tense.

In English, we say either 'would play' or 'used to play' to express something we habitually did in the past. The 'would' used in this aspect should not be confused with the 'would' used to describe hypothetical or probable situations. That is expressed with the conditional mood.

Your first sentence correctly conveys the habitual past.
It can also be rendered:Cuando (era) pequeño, solía jugar al fútbol.